Casino gaming device with reverse pay table logic

ABSTRACT

A computerized wagering game apparatus for wagering by a player has at least a game controller having a processor, memory, a random number generator and game logic generating winning and losing outcomes with assigned probabilities. For any single wager event, the probability for a winning wager outcome is greater than the probability for a losing wager outcome while maintaining a house retention on wagers by the game apparatus which is greater than 0% of all wagers. The house retention wager is effected by the apparatus decrementing a player account or machine credit without the player specifically placing that account or credit in play for the single wager event.

RELATED APPLICATION DATA

This application claims the benefit under 35 U.S.C. §119 (e) ofprovisional application Ser. No. 60/815,027, filed 20 Jun. 2006.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates to gaming play and especially computerized casinowagering devices implementing novel wagering formats. Novel wageringformats encompass relatively high probability wins with moderated winamounts and relatively larger, lower probability losses.

2. Background of the Art

Games of chance have been enjoyed by people for thousands of years andhave enjoyed increased and widespread popularity in recent times. Aswith most forms of entertainment, players enjoy playing a wide varietyof games and new games. Playing new games adds to the excitement of“gaming.” As is well known in the art and as used herein, the term“gaming” and “gaming devices” are used to indicate that some form ofwagering is involved, and that players must make wagers of value,whether actual currency or some equivalent of value, e.g., token orcredit.

One popular game of chance is the slot machine, which includes bothphysical reels and video game play with virtual reels. Conventionally, aslot machine is configured for a player to wager something of value,e.g., currency, house token, established credit or other representationof currency or credit. After the wager has been made and the amount ofthe wager is placed at risk, the player activates the slot machine tocause a random event to occur. The player wagers that particular randomevents will occur that will return value to the player. A standarddevice causes a plurality of symbols to be distributed on the screen,typically by causing physical or virtual reels to spin and ultimatelystop, displaying a random combination of some form of indicia, forexample, numbers or symbols. If this display contains one of apre-selected plurality of winning combinations, the machine releasesmoney into a payout chute or increments a credit meter by the amount wonby the player. For example, if a player initially wagered two coins of aspecific denomination and that player achieved a payout event, thatplayer may receive the same number or multiples of the wager amount incoins of the same denomination as wagered. If no winning event occurs,the player forfeits the amount of the initial wager. Bonus events mayalso occur when there is a bonus triggering event according to rules ofthe game.

This historical limitation of using physical coins or tokens for playerwagers and the dispensing of player awards is the fundamental reason whythe award values of gambling devices were historically designed to bemultiples of the player wager amount (e.g., 1×, 2×, 3×, etc.). Eventhough this requirement of having to deal with whole coin or tokenamounts no longer exists for the modern day gambling device, thetraditional method of awarding multiples of the wager amount remainsfirmly in place today.

Multi-line games exist today with the capability of awarding partialpayouts but fundamentally each line operates awarding a multiple of thebet amount. The combination of multiple lines, each paying an integermultiple of the bet amount, with some lines winning and others losingcan in some circumstances create an award that is not a multiple of abet amount but this is a consequence of the multi-line capability of themachine with each pay line still paying multiples of the original betamount as applied to individual pay lines. Because payouts includemultiples of the original wager and the casino must retain an overallprofit from the wagering, the frequency of wins to losses must be lessthan 1:1, providing a higher frequency of losing events, which isdispleasing to players.

There are many different formats for generating the random display ofevents that can occur to determine payouts in wagering devices. Thestandard or original format was the use of three reels with symbolsdistributed over the face of the reel. When the three reels were spun,they would eventually each stop in turn, displaying a combination ofthree symbols (e.g., with three reels and the use of a single payoutline as a row in the middle of the area where the symbols aredisplayed.) By appropriately distributing and varying the symbols oneach of the reels, the random occurrence of predetermined winningcombinations can be provided in mathematically predeterminedprobabilities. By clearly providing for specific probabilities for eachof the pre-selected winning outcomes, precise odds that would controlthe amount of the payout for any particular combination and thepercentage return on wagers for the house could be readily controlled.Control of the frequency and amount of winning events is effected byphysical mapping of reels or electronic mapping of symbols.

Other formats of gaming apparatus that have developed in a progressionfrom the pure slot machine with three reels have dramatically increasedwith the development of video gaming apparatus. Rather than have onlymechanical elements such as wheels or reels that turn and stop torandomly display symbols, video gaming apparatus and the rapidlyincreasing sophistication in hardware and software have enabled anexplosion of new and exciting gaming apparatus. The earlier videoapparatus merely imitated or simulated the mechanical slot games in thebelief that players would want to play only the same games. Early videogames therefore were simulated slot machines. The use of video gamingapparatus to play new games such as draw poker and Keno broke the groundfor the realization that there were many untapped formats for gamingapparatus. Now casinos may have hundreds of different types of gamingapparatus with an equal number of significant differences in play. Theapparatus may vary from traditional three reel slot machines with asingle payout line, video simulations of three reel video slot machines,to five reel, five column simulated slot machines with a choice oftwenty or more distinct pay lines, including randomly placed lines,scatter pays, or single image payouts, and even fifty to 100 line playsfor poker games. In addition to the variation in formats for the play ofgames, bonus plays, bonus awards, and progressive jackpots have beenintroduced with great success. The bonuses may be associated with theplay of games that are quite distinct from the play of the originalgame, such as the video display of a horse race with bets on theindividual horses randomly assigned to players that qualify for a bonus,the spinning of a random wheel with fixed amounts of a bonus payout onthe wheel (or simulation thereof), or attempting to select a random cardthat is of higher value than a card exposed on behalf of a virtualdealer.

A video terminal is another form of gaming device. Video terminalsoperate in the same manner as conventional slot or video machines exceptthat a redemption ticket is issued rather than an immediate payout beingdispensed.

Casino games of chance also take the form of table games. The latterinclude games such as Black Jack, Roulette, Craps and Baccarat. Tablegames offer a very different gambling experience than the typical slotmachine. With table games, it is common for the player to place multiplewagers on various game outcomes, with the intention of “spreading theirodds” across multiple outcomes with the intent of covering the losingbets with the awards received from the winning bets. The game of crapstakes this philosophy to a unique extreme by presenting multiple gameoutcome events to the player during the same base wager cycle. Unlikethe single line slot machine experience, the table game experience,particularly craps, offers the player a very different perspective ofexpecting higher probability incremental gains from the base wager, withthe possibility of losing their entire bet amount as a result of anygame outcome. This is somewhat akin to the multi-line slot machineexperience where although each individual award pays a multiple of thebase bet amount, the overall pay per wager event may in some cases be afractional amount due to the number of wins or losses of individual betscomprising the overall wager. The psychology of the typical slot machineas compared to that of table games is oriented towards low probabilitylarge awards balanced by high probability small, losing outcomes.

A probability distribution assigns a probability to every interval ofreal numbers along the real number line, such that a) every possibleinterval has a probability greater than or equal to zero, b) the totalprobability for any outcome is one, and c) the probability of the unionof one or more disjoint intervals equals the sum of the probabilities ofthose intervals. For a random variable X derived from a givenprobability distribution, the mean and standard deviation can becalculated from the moments of the probability density function, andfrom Chebyshev's inequality (below) the probability that a certainoutcome lies greater than k standard deviations from the mean is lessthan 1/k².

An embedded gaming device with a set of possible wagering outcomes canbe viewed as a system for implementing a probability distribution fornet winning or net losing game outcomes. For each game outcome, the netoutcome is the game win amount minus the bet amount. Together, the netoutcome (each outcome being a net win or alternatively a net loss if thewin is less than the bet) amounts create a distribution from which canbe obtained an expected or mean outcome and a standard deviation forpossible outcomes.

From Chebyshev's inequality we know that for the embedded gaming devicewith mean μ and standard deviation σ,

-   -   No more than ½ of the possible net outcomes are greater in        magnitude than sqrt(2)*σ from the mean outcome μ. Equivalently,        at least ½ of the net outcomes are less in magnitude than        sqrt(2)*σ from the mean outcome.    -   No more than ¼ of the possible net outcomes are greater in        magnitude than 2σ from the mean outcome μ. Equivalently, at        least ¾ of the net outcomes are less in magnitude than 2σ from        the mean outcome.    -   No more than 1/9 of the possible net outcomes are greater in        magnitude than 3σ from the mean outcome μ. Equivalently, at        least 8/9 of the net outcomes are less in magnitude than 3σ from        the mean outcome.

In a profitable casino embedded gaming device a constraint on theoverall mean net outcome μ (or expected net outcome) is that theretention of wagers by the casino gaming device must be greater than 0%,or equivalently, the mean net outcome μ for the player will be less than0 in order to guarantee a profit for the casino.

SUMMARY OF THE INVENTION

A wagering game is provided with increased frequency of net winningevents as compared to net losing events. Increased frequencies of netwinning events are balanced by moderation of potential winning amountsand relatively larger losing amounts with correspondingly decreasedfrequency. A wagering game may be played in which frequencies of winsare increased but with amounts of potential losses increased aboveamounts won so that even though numerical frequencies of payoutsincrease, the house may maintain sufficient retention rates to continuea profit on the game.

DESCRIPTION OF THE FIGURES

FIG. 1. Example Conventional Prior Art Pay Table. Conventional pay tableshowing probability of a net winning outcome is less than theprobability of a net losing outcome and the net win amounts greater thanthe net loss amounts.

FIG. 2. Example Conventional Prior Art Pay Table Chart. A chart showingthe distribution of game outcomes for a conventional prior art systemwith outcome probability indicated along the X axis and payout along theY axis.

FIG. 3. Example Conventional Prior Art Payout Graph. Conventional gamesof the prior art offset frequent small losing outcomes with relativelyrare large winning outcomes.

FIG. 4. Example Reverse Logic Pay Table. Reverse logic pay table showingprobability of a net losing outcome is less than the probability for anet winning outcome and the net loss amounts are greater than the netwin amounts.

FIG. 5. Example Reverse Logic Pay Table Chart. Chart illustrating thedistribution of game outcomes for a reverse logic pay table system withoutcome probability indicated along the X axis and payout along the Yaxis.

FIG. 6. Example Reverse Logic Payout Graph. The system of the inventionis characterized by frequent winning outcomes offset by relatively rarelarge losing outcomes.

FIG. 7. Example Catastrophic Losing Outcome. Illustrates a catastrophiclosing outcome consistent with the system of the invention where aplayer might lose the entire credit balance.

DETAILED DESCRIPTION OF THE INVENTION

As discussed above, the characteristics of prior art casino slot machinegaming devices include: they are based on a bet amount wagered per game,a pay table that pays back a fixed percentage over time, single line winamounts that are multiples of the wager amount, and the potential for abig win either in the base game pay table or in some forms by adding aplurality of bonus screens on top of the base game. The presenttechnology includes systems, methods, apparatus and rules thateffectively reverse probabilities or frequencies of winning and losingevents and shifts scales of potential winning and losing amounts so thatthe “house” still statistically returns less than 100% even with higherfrequencies of winning events as compared to losing events, even withnominally consistent or constant amounts of wagers. These reverseprobabilities and payouts can be effected in a number of alternativemanners, both in physical games (by applying game rules that impactprobabilities) and in computerized games (with random number generators,mapped symbol provisions, and pay tables impacting the reverse paybackevents).

The following descriptions will provide enablement for numerousalternatives for practice of the present technology.

A first format for enabling practice of the present technology can bedescribed as establishing probabilities and amounts of payouts andlosses such that ΣWn·An−ΣLn·Sn<0 wherein Wn is the frequency(probability) of a net winning event for each probable winning eventwithin the total set of events n, A is the payout amount of each winningevent within all of the probable events n, Ln is the frequency(probability) of a net losing event for each losing event within allprobable events n, and S is the loss amount for each losing event withinall probable events n, wherein ΣWn>ΣLn. In non-mathematical terms, thesum all of the individual probabilities for each winning eventmultiplied by the individual payout for each winning event is less thanthe sum all of the individual probabilities for each losing eventmultiplied by the individual loss effect for each losing event, andwherein the total probability of winning events W is greater than thetotal probability of losing events.

One embodiment of the present technology consists of an embedded casinogaming device with a set of possible wagering outcomes viewed as asystem for implementing a probability distribution for net winning ornet losing game outcomes. For each game outcome, the net win is the netincrease in the player's monetary or credit balance due to the game'soutcome, taking into account the wager, outcome and any bonusing or sidebets. Together, the net win (or alternatively net loss if the player'smonetary or credit balance decreases due to the game's outcome) amountscreate a distribution from which can be obtained a mean or expected netoutcome μ and a standard deviation σ for all possible outcomes. Thetotal set of net outcomes is divided into a set of relatively largemagnitude outcomes consisting of those net outcomes greater than orequal in magnitude to μ+sqrt(2)*σ (that is √2*σ) or less than or equalin magnitude to μ−sqrt(2)*σ, and a set of relatively small magnitudeoutcomes consisting of those net outcomes greater than μ−sqrt(2)*σ andless than μ+sqrt(2)*σ. A fundamental requirement for the casino gamingdevice is the expected net outcome μ for the entire distribution(including bonusing) must be less than zero for the casino to make aprofit. Using Chebyshev's inequality as a basis (choosing k=√2) theteachings of the present technology predict that the expected netoutcome for the set of relatively small magnitude outcomes is greaterthan zero. Correspondingly, the expected net outcome for the set ofrelatively larger magnitude outcomes must be less than zero to result inan overall mean for the gaming device that is less than zero.

Another alternative embodiment consistent with this technology would bethe Paid-to-Play format described herein. In the Paid-to-Play format,here exemplified with a poker variant against a pay table, it will beassumed that a player begins play with 100 credits. The gaming system orcasino table will “pay” the player 5 credits to play, so that as thefirst set of cards is dealt, the player immediately has 105 credits, asopposed to normal play where the player has 5 credits at risk and 95credits in reserve. If the player attains a hand over a certain rank(e.g., over a rank of at least queen high in five card stud (which willoccur about 56% of the time), the player will be paid an amountproportional to the wagered amount (e.g., if paid 1:1, the player couldreceive 5 credits and the reserve would be 110 credits). Higher rankedhands would receive higher payouts (higher odds) based on the amount ofthe payment to the player.

At the same game event, low ranking hands would effect losses to theplayer out of the player reserve. For example, a perfect “low” hand of6, 4, 3, 2 and Ace (of more than one suit) could cause a loss of theentire 100 credits. Even though the frequency of winning events (anon-loss is a “net win” due to the “reverse” wager of 5 credits paid tothe player by the casino) significantly exceeds then frequency of losingevents, the house advantage can be retained within acceptable rangesbecause of larger absolute loss amounts. Again, some capability ofassuring credits that will cover maximum losses, or “wagers” for thePaid-to-Play format payment may be limited within ranges of multiples ofavailable credit, just as wagers are limited to available credits. Forexample, if the largest catastrophic loss is 20×, the maximum wager(payment) allowed would be 5 units with 100 credits available, 4 unitsfor 80-99 credits available, 3 units for 60-79 credits, 2 units for40-59 credits available, and 1 unit for 0-39 credits. It is alsopossible to grant some leeway in the range of available credits asgratis for losses so that a player with 75 credits available may wager 4credits, even if a catastrophic loss cannot be fully covered by theavailable credits. It is also possible that such games may be limited inplay to players with an account which may be drawn down, over the amountin play on the device or on the table. Other ways to allow play forplayers with a small credit balance is to offer an “insurance” cover betwhich for a fixed wager amount (or deduction in the “paid to play”amount) would “insure” the player in the event of a catastrophic loss.

A general description of the apparatus and methods according to thepresent technology can be provided as a computerized wagering gameapparatus for use by a player, comprising: a game controller having aprocessor, memory, and a random number generator; the game controllergenerating symbols and outcomes for wagering events in the game; eventsin the game providing statistically expected numbers of observed (net)winning events that are greater in frequency for the player thanstatistically expected numbers of observed (net) losing events for theplayer; wherein statistical retention of wagers by the gaming apparatusis greater than 0% for the game. This means that the statistical returnto a player (always considered over a theoretic infinite number ofplays) is less than 100%.

An alternative description is a computerized wagering game apparatus foruse by a player, comprising: a game controller having a processor,memory, a random number generator; the game controller providing a totalset of event outcomes consisting of a set of possible net tying eventoutcomes, net winning event outcomes and net losing outcomes; whereinthe total set of event outcomes comprises a probability distribution forpossible game outcomes wherein for k>=√(2) (that is, square root of 2)there is a greater probability of losing outcomes than winning outcomesconsidering only those outcomes that lie greater than k standarddeviations from the overall distribution's mean outcome. Bonusing events(e.g., a triggering event where there may or may not be any implicationon the underlying value placed at risk in the basic game) are inherentlyincluded with the tying, winning and losing events. The mean outcome isthe statistical expected value of game outcomes and may lie very closeto a net tying event (such as with a game with a 98% payback). Forexample purposes, pay tables given in the figures show a game withexpected 100% return in which case the tying event is equal to theexpected value, but it should be understood that in reality the meanoutcome for a casino game is designed to be weighted in favor of thecasino.

The unique orientation of winning events and losing events in theirprobabilistic relationship offers an opportunity for a unique gamingevent, as part of an automatic bonus event or as a side bet bonus event.The bonus event, because of the higher probability of winning events,has an especially attractive feature. Bonuses can be paid on the basisof extended numbers of consecutive winning events, again either as anautomatic bonus event or as a side bet bonus event. For example, with 10consecutive non-loss events (pushes as well as wins) in a row, therecould be an automatic win of $10.00, or if based on a side bet bonusevent, where the system is receiving higher revenue inputs and so higherpayouts might be available, a $25 bonus might be available. Similarlywith fifteen consecutive wins, $15 or $50, respectively, with twentyconsecutive wins, $100 and $500, respectively and the like, up toactuarially tolerable award amounts. Additionally, players might electto enter such a bonus event midstream if they feel they are in a hotstreak, with attendant reduced awards for the bonus. For example, afterthree consecutive wins, the player may be able to place the $0.25 sidebet entry fee, and if seven more consecutive non-loss events occur, theplayer could receive a educed amount, such as $6 or $7, the basis of thebonus still being the ten consecutive non-loss events, but with thelower payback because of the later entry into the event. One point ofattractiveness of the bonus event is that because of the higherfrequency of winning events versus losing events in the game, there is aclearly higher probability for such consecutive win events to occur. Thevideo system could, for example, make a running display of the count ofconsecutive wins for present and/or recent play (as with a baccaratdisplay (showing Banker or Player wins) or roulette display (showing Redor White, Odd or Even) to further entice players into making a side betwager or at least playing the game. The display could also provideinformation on the number of bonus winning streaks occurring in the pasttwenty-four hours and how long those streaks were and the theoreticpayouts for those streaks.

Another alternative apparatus description may be as a computerizedwagering game apparatus for wagering by a player, comprising: a gamecontroller having a processor, memory, a random number generator; thegame controller providing a set of possible game outcomes consisting ofnet tying outcomes, net winning outcomes and net losing outcomes,wherein the set of total game outcomes consists of a probabilitydistribution for all possible game outcomes; wherein for k=√(2) there isa greater probability of a winning outcome than losing outcomeconsidering only those outcomes that lie less than k standard deviationsfrom the overall distribution's mean outcome.

A still further alternative description could be as a computerizedwagering game apparatus for wagering by a player, comprising: a gamecontroller having a processor, memory, a random number generator andgame logic generating winning and losing outcomes with assignedprobabilities, wherein for any single wager event the probability for anet winning wager outcome is greater than the probability for a netlosing wager outcome while maintaining a house retention on wagers bythe game apparatus which is greater than 0% of all wagers.

Yet another alternative description may be as a computerized wageringgame apparatus for wagering by a player, comprising: a game controllerhaving a processor, memory, a random number generator, game logiccapable of generating winning and losing outcomes with assignedprobabilities, and accounting logic capable of tracking the player'scredit balance, wherein for a single wager event the probability of aplayer's credit balance increasing as a result of a game round isgreater than the probability of a player's credit balance decreasing asa result of a game round while maintaining a house retention on wagersby the game apparatus which is greater than 0% of all wagers.

Yet another alternative description may be a player credit-bankedcomputerized wagering game apparatus for wagering by a player,comprising: a game controller having a processor, memory, a randomnumber generator, game logic capable of generating winning and losingoutcomes with assigned probabilities, and accounting logic capable oftracking the player's credit balance to sources within local apparatusand within external wagering game apparatus credit-processing apparatus,wherein initiating play of a round of a game adds a wager amount to theplayer's credit balance and the game logic assigns varying probabilitiesand amounts for losing outcomes to the player's credit balance such thathouse retention on wagers on the game apparatus is greater than 0% ofall wagers.

What is meant by the terminology external wagering game apparatuscredit-processing apparatus is that a processor other than the gamecontrol apparatus and a processor outside the physical confines of theterminal or slot machine or game table manages credit. As opposed tomachines where credit is directly established by monetary input, ticketinput, voucher input or the like, credit here may include or consist ofaccess to an account, such as one managed by the casino or a chain ofcasinos. In those environments where wagering is allowed directly oncredit cards, debit cards, cash cards or to bank accounts, this wouldsuffice for the external wagering game apparatus credit-processingapparatus.

A method of playing a wagering game may be described as comprising: aplayer initiating play of the wagering game by placing value at risk.The risk may be achieved by placing a wager, by the system “paying” theplayer to play (as described elsewhere herein) or just by initiating agame which automatically places money/credits at risk and increments ordecrements money/credits based on results, independent of defining asingle round wager amount. At least the player receives randomlyprovided sets of symbols for use in the game. A dealer (real or virtual)may also receive a set of symbols if the game includes aplayer-versus-dealer competition as opposed to or in addition to aplayer-versus-paytable event. The player's received randomly providedset of symbols is evaluated (e.g., compared to a dealer's hand and/oragainst ranking or designated count or designated order, or designatednumbers of specific symbols, such as 1 cherry, two cherries, three bars,etc.) according to at least one of predetermined rules of count (e.g.,as in baccarat, Twenty-One, 7.5 and 21.5 poker), order (e.g., threejackpot symbols in a single line, a name spelled out in order, etc.),sets (e.g., any three bars, a flush, etc.), matching symbols, rank ofsymbols (e.g., poker hands), rank of combination of symbols (pokerhands), alignment of symbols (e.g., sequences of numbers is hierarchalorder, a scene formed in logical order, etc.), and numbers of triggeringsymbols (e.g., three bonus symbols in any position on a screen). Theevaluation assigns net tying outcomes with tying effect (no creditadjustment from before starting round of play of the game), net winningoutcomes with winning effects (e.g., the positive change in total creditposition, and inclusive of the common use of returning the creditposition to the total credit available before start of the game whencredit has been reduced to allow start of the game) and net losingoutcomes with losing effects (e.g., a reduction in total creditavailable comparing credit after conclusion of a round of play to creditavailable before the round of play) to all possible received randomlyprovided sets of symbols. Frequency of net winning outcomes for theplayer exceeds frequency of net losing outcomes for the player, andstatistical magnitude of winning effects and magnitude of losing effectsunder the rules for the game statistically assure house retention onwagers that is greater than 0% of all wagers. In this method, symbolsare randomly provided by physical playing cards, spinning of a physicalreel on a slot machine, and/or by a random number generator providingsymbols on a display screen. The player may place value at risk byplacing a wager of a player-selected amount on a round of play of thewagering game, and/or by a processor allotting a player-selected amountof credit to the player's credit while placing at risk an amount ofcredit greater than the player-selected wager amount. A system may havean automatic default amount at risk and reward (e.g., a player may notbe able to select amounts at risk, except for underlying credit unitsplaced at risk, as in playing a $1.00 machine with all factors of winsand losses being based on the unit amount of $1.00). Similarly, theplayer may select an automatic $0.25 wagering device or a $5.00 wageringunit device. The player may or may not be able to alter the number ofunit credits wagered within the system. That is, if a player is on a$5.00 unit credit machine, he may be required to stay at the $5.00 levelfor all wagers, or he may be able to alter the unit credits at risk inany round of play by increasing the $5.00 amount or decreasing the $5.00amount at any time before initiation of play. The method may use astatistical basis for game play wherein summation of probabilities ofnet winning events multiplied by winning payback odds for each winningevent is less than summation of probabilities of net losing eventsmultiplied by losing deduction odds for each losing event. It ispossible, if not preferred to have a frequency of net winning eventsplus frequency of net tying events that exceeds 60% of all wageringoutcomes, such that in at least 60% of rounds of play, the player willnot lose any value. The method may also be provided such that thefrequency of net winning events exceeds 60% of all wagering outcomes(e.g., ties may or may not be considered in this comparison). The methodmay be practiced with at least one net losing event having a magnitudeor loss effect that exceeds at least the magnitude of at least 90% ofall net winning events. That is, even though a nominal wager of forexample $5.00 is placed, and 90% of all winning outcomes returns $50.00or less, at least one losing outcome at the $5.00 nominal unit creditwagering amount will cause a net loss of greater than $50.00, such as atleast $51.00.

As noted, the system may be provided as a processor-based or computersystem with direct input into a terminal, hand-held devices forinterfacing with the processor, television input from rooms, or internetplay. Buttons or touch screens or keyboards may be used for playerinput. In a further non-limiting configuration, one or more of theplayers can be located in separate locations, and the player terminalsor hand-held devices or player screens in rooms can be connected to thecontroller via communication links (e.g., hardwired or wireless).Standard protocols, software, hardware and processor languages may beused in these communication links, without any known limitation. Thereare hundreds of available computer languages and formats that may beused, among the more common being Ada; Algol; APL; awk; Basic; C; C++;Cobol; Delphi; Eiffel; Euphoria; Forth; Fortran; HTML; Icon; Java;Javascript; Lisp; Logo; Mathematica; MatLab; Miranda; Modula-2; Oberon;Pascal; Perl; PL/I; Prolog; Python; Rexx; SAS; Scheme; sed; Simula;Smalltalk; Snobol; SQL; Visual Basic; Visual C++; and XML.

Any commercial processor may be used either as a single processor,serial or parallel set of processors in the system. Examples ofcommercial processors include, but are not limited to Merced™, Pentium™,Pentium II™, Xeon™, Celeron™, Pentium Pro™, Efficeon™, Athlon, AMD andthe like.

Display screens may be segment display screen, analog display screens,digital display screens, CRTs, LED screens, Plasma screens, liquidcrystal diode screens, and the like.

A pay table can typically be presented as game outcomes in tabularformat by rows where each row in the table has a probability ofoccurrence and an associated amount. An simplified example pay table forconventional prior art casino slot machine gaming devices is presentedin FIG. 1. In the figure, for purposes of example the bet amount isassumed to be 1, and the outcomes are ordered from lowest payout tohighest payout in multiples of the bet amount. The net win amount is thepayout amount minus the bet amount (and may be a net loss if the resultis negative). Note that in this particular example, there is an outcomewith net parity (bet equals payout) but there is nothing requiring sucha row in any pay table.

It can be seen that the expected net win for the pay table in FIG. 1 iszero (assuming a bet amount of $1 and summing the net outcome amountsweighted by probability of occurrence as shown in column 4) In a typicalcasino however, the pay tables will be offset such that there will be ahouse advantage that will result in the expected payout to the playerbeing less than even money. Typical values for the house advantage in atypical casino may range from 80% to 98% for example, but is variablebased on gaming jurisdiction and casino. Another way of stating this isthe expected net win amount will be less than zero, or alternatively,the retention of wagers by the casino will be greater than 0 on apercentage basis.

In the pay table in FIG. 1, it can be seen that the payout structure hasbeen designed so that the game will play with a frequent amount oflosing outcomes interspersed with relatively rare large wins. Ingeneral, this is what gives the prior art casino slot machines theircharacteristic look and feel of play.

It can be seen from FIG. 1 that the probability of a win outcome is 13%(4%+3%+2%+2%+1%+1%) while the probability of a net loss is 80%. 7% ofthe possible outcomes result in a net even outcome (bet equals winamount). Using this terminology, “net win” refers to the increase in theplayer's credit balance derived from the combination of the bet amountand the outcome of the wager, i.e., the win amount of the wager minusthe amount of the wager itself. If a player bet $1 and won $10, the netwin would be $10 payed−$1 wagered=$9 net win. If the wager did notresult in a win, the net loss would be the amount of the wager itself,i.e., the $1 that was risked by the player for the wager.

FIG. 2 illustrates the example conventional pay table in graphical form.The winning outcomes 201 are relatively rare events indicated by thewidth of the winning outcomes in the graph. These wins are offset by thelosing outcomes 202 that have a much higher probability of occurrencebut a smaller payout magnitude. Together, the winning outcomes and thelosing outcomes can be averaged to obtain a mean outcome, and this meanoutcome gives the expected win (loss) for the pay table (and hence thegaming device). For example purposes, the illustrative pay table ofFIGS. 1 and 2 has been designed to have a mean outcome of zero, but inan actual casino the mean outcome will be shifted in the casino's favor.Nothing in the system of the invention requires the overall mean outcometo lie in any certain range with respect to the individual potentialwagering outcomes (although to be profitable for the casino the meanoutcome of the pay table should be less than zero), rather, here we aretalking about the manner in which the relatively rarer, larger magnitudeoutcomes relate to the properties of the distribution as a whole.

The mean net outcome and standard deviation can be calculated from thepay table in FIG. 1 using well known formulas to yield 0 for the meanand 3.0364 for the standard deviation. The set of net outcomes withmagnitude greater than μ−√2σ and less than μ+√2σ (greater than −4.2942and less than 4.2942) consists of the first four lines of the pay table.The mean value of these outcomes is −1*0.8+0*0.07+1*0.04+4*0.03=−0.64and we see that the pay table of FIG. 1 is not consistent with thesystem of the invention because the resultant mean value of therelatively lower magnitude outcomes is not greater than zero. Similarly,the mean net outcome for the set of relatively large outcomes (withmagnitude greater than or equal to sqrt(2)*σ from the mean) is +0.64 andis not less than zero as required by the system of the invention.

FIG. 3 gives a sample payout graph over time for a game implementing aconventional pay table. Each point on the graph indicates the player'sbalance at a particular point in time, with time being indicatedindirectly on the x-axis through the number of wagers. It can easily beseen from the chart that the most likely payout is a loss, indicated bythe tendency for the payout line segments connecting sequential dots inthe graph to be directed with a negative slope. Interspersed with thehigh probability losses are low probability high magnitude winningoutcomes 301 that infrequently boost the player's credit balance withlarge wins, bonuses or jackpots.

The system of the invention introduces a reverse or in some embodimentsa partial pay paradigm to provide for a gaming device with uniquecharacteristics and certain advantages over prior art systems. It doesthis by reversing the high and low probability events to result in a paytable that consistently rewards the player with small wins at the riskof low probability large (potentially catastrophic) losses.

FIG. 4 gives an example reverse logic pay table consistent with thesystem of the invention. A quick comparison to the pay table of FIG. 1reveals that the pay table has simply been “reversed”—the wins have beenreplaced with losses, and vice-versa, to illustrate that most existingslot machines could potentially be converted to a reverse logic paytable (assuming that the mean outcome is adjusted to result in a net winfor the casino and not the player. For these examples the mean isalready at zero and so such an adjustment does not need to be performed.This does not affect the validity of the examples however). FIG. 5 showsa chart illustrating the pay table from FIG. 4. Characteristic of such apay table are there are fewer large winning outcomes, and mainly largelosing outcomes.

Psychologically, a game machine built with a pay structure of the systemof the invention rewards the player with constant positive reinforcementbecause the credit balance on the machine has a higher probability ofincreasing with each spin. For players used to seeing their creditbalance decrease with each spin at conventional gaming devices in acasino, the result is potentially a refreshing break from the steadydrain on credits associated with those conventional prior art gamingdevices. Comparing FIG. 2 and FIG. 5 clearly illustrates the fundamentaldifference in payout characteristics as they relate to the system of theinvention and prior art gaming devices. In FIG. 2, the wins are the lowprobability (thin) high magnitude (tall) events. In FIG. 5, this isreversed with the losses being the low probability high magnitudeevents.

The mean net outcome and standard deviation can be calculated from thepay table in FIG. 4 using well known formulas to yield 0 for the meanand 3.0364 for the standard deviation. The set of net outcomes withmagnitude greater than μ−√2σ and less than μ+√2σ (greater than −4.2942and less than 4.2942) consists of the first four lines of the figure.The mean value of these outcomes is 1*0.8+0*0.07+−1*0.04+−4*0.03=0.64and we see that the pay table of FIG. 4 is consistent with the system ofthe invention because the resultant mean value of the relatively lowermagnitude outcomes is greater than zero. Similarly, the mean net outcomefor the set of relatively large outcomes (with magnitude greater than orequal to sqrt(2)*σ from the mean) is −0.64 and is less than zero asrequired by the system of the invention.

FIG. 6 illustrates a payout graph for a reverse logic pay table. It canbe seen during game play the player's credit balance has a highprobability of increasing with incremental wins, interspersed with largelow probability losing outcomes 601.

In one embodiment of the system of the invention, a casino game isprovided that does not require the player to wager any amount to play,rather, the player adds a base amount of credits into the machine thatrepresent the credit amount the player wants to risk. This amountbecomes the player's credit basis for the wagering session. With eachspin in a reel game (or equivalent terminology applied to non-reelgames), the casino pays the player what is termed a “reverse wager”. Thereverse wager is an amount the casino or house pays to the player everytime the spin button is pressed and in some embodiments is based on orderived from the player's credit basis in the machine. In essence theplayer and the casino's roles have reversed and the casino is paying theplayer to play, and the casino wins (the player loses) when aninfrequent rare event happens with a large payout.

Instead of a steady series of losses and the possibility of a large winassociated with systems of the prior art, the casino game of the systemof the invention provides for the probable guarantee of a relativelysteady credit increase but provides for the possibility of acatastrophic loss. Instead of the traditional mentality when playing aslot hoping for the lucky rare event, a player playing a reverse paytable device hopes for the random outcome because the (un)lucky lowprobability events are usually losses.

In some embodiments of the system of the invention there are no winningawards. Instead there is only the possibility of various loss amounts tobe subtracted from the player's credits. Other embodiments provide for avariety of wins and/or losses combined into a single pay table wherebyadding the possibility of a large loss into the payout structure of thegame allows the game designer to simultaneously provide forcorrespondingly larger wins on the same machine. Such a machine has thereverse pay table of the system of the invention combined with atraditional prior art pay table, although win amounts will be lessfrequent or less in magnitude than losing amounts consistent with thesystem of the invention.

Other embodiments of the system of the invention that may be morepalatable in certain jurisdictions provide for a gaming device thatrequires a base buy-in amount from the player equal to the amount of thelargest possible loss and with each wager that base buy-in amount isrisked by the player. Wins are awarded using a pay structure based onthe base buy-in amount and the probability structure of the pay tablesuch that most of the time the total buy-in amount is awarded back tothe player including an incremental amount determined from the basewager amount, but, in relatively infrequent occasions there is a largeloss and only a fraction of the wager is awarded to the player. Whenconsidered in light of net game outcomes there is no difference in thenet win/loss structure between the two forms, but in this embodiment thewager is presented in a manner that may conform better to the currentletter of the law in certain gaming jurisdictions requiring a player betand casino payout.

To further illustrate this type of embodiment of the system of theinvention, the pay table of FIG. 4 shows that there are several ways toimplement the actual game. For example, Game A might have the casino paythe player $1 per spin event, with the player losing up to $20 in onespin. Thus, for Game A, the casino pays the player a $1 reverse bet onevery wager. The maximum $20 outcome is a loss (win for the casino)based on the wager outcome. Alternatively, for Game B implemented usingtraditional wagering terminology, the player bets $20 per spin and themax win for the player is $21. The catastrophic loss where the playerloses the entire $20 bet can only happen 1% of the time for this examplepay table. Game B uses traditional wagering terminology that may be insome cases more acceptable to certain jurisdictions. It can be easilyseen that the differences between the two games are due purely toterminology, with no discernible differences in the payouts for netwinning or net losing outcomes between the two games. It is important tonote that in order to implement Game B, a fractional payout must beassigned to the wager ($21 pay for $20 bet, etc.). In any case, thesetwo embodiments of the system of the invention present here areequivalent when viewed in terms of the net win and net loss for thevarious outcomes and the respective probabilities for such.

Most existing game formats can be adapted for use with the system of theinvention. For example, a game device of the system of the invention cantake the form of a one line reel spinning game, either mechanical orvideo, a multi-line reel spinner, mechanical or video, a keno videoapparatus, or other form. The actual presentation comprising video,sound or other multimedia can be implemented in any of a multitude ofchoices and still have the pay table characteristics of the system ofthe invention.

Taking a single line reel spinning game as a specific embodiment forexample purposes only, a game implemented using a pay table of thesystem of the invention might have bombs or other symbols with anegative connotation. The player, when playing such a device, would hopefor a random no-pattern wager outcome, which means he would keep thecasino's “bet”. In the event where three bombs lined up in a row (acatastrophic outcome as shown in FIG. 7), the player might lose a) hisentire credit balance on the device, b) a maximum percentage (e.g., 50%of total credits available above a threshold minimum amount, for exampleabove a minimum number of credits such as 100), or in c) someembodiments, the loss might be limited to the initial buy-in amount onthe game machine. Example c) may operate such that if a player has from1-100 credits available, all credits will be lost, and if 101 to 200credits are available, only 100 credits will be lost, and for a numberX>200 credits, some specific percentage such as 50% X will be lost. Sucha catastrophic outcome in pay table structure does not exist in casinoslot machine devices currently operating on casino floors but adds acompelling, exciting feel and an entirely new psychology to the game. Assuch, it is expected that a game consistent with the system of theinvention will likely appeal to a different segment of player.

Some embodiments of the system of the invention might include acombination of both reverse pay tables and regular pay tables in amulti-game format. A player might play for the big win for a period oftime, then switch to play for the incremental win as a refreshing changein odds structure. This could be done by a player exercising an optionon underlying probability strategies. For example, the gaming apparatusmight display to selectable play formats with the same symbols, and theselection of one format of a given game versus another format of thesame game would alter the game format from the higher frequency winevent with reduced average size payout to a lower frequency win eventwith higher average size formats as compared to the other format (withthe higher win frequency).

It is to be noted that although numerous specific examples have beengiven to assist in an appreciation and understanding of the genericconcepts of this disclosure and inventions included therein, theexamples are not intended to be limiting with respect to the claims andthe scope of the invention.

1. A computerized wagering game apparatus for wagering by a player,comprising: a game controller having a processor, memory, a randomnumber generator and game logic capable of generating at least one netwinning or net losing outcome with assigned probabilities, wherein forany single wager event the probability for a net winning game outcome isgreater than the probability for a net losing game outcome whilemaintaining a house retention on wagers by the game apparatus which isgreater than 0% of all wagers.
 2. The wagering game apparatus of claim 1with accounting logic capable of tracking the player's credit balance,wherein for a single wager event the probability of a player's creditbalance increasing as a result of the single wager is greater than theprobability of a player's credit balance decreasing as a result of thewager.
 3. The wagering game apparatus of claim 2 wherein the probabilityof a player's credit balance increasing as a result of the single wageris greater than 60 percent.
 4. A player-banked computerized wageringgame apparatus for wagering by a player, comprising: a game controllerhaving a processor, memory, a random number generator, game logiccapable of generating game outcomes with assigned probabilities, andaccounting logic capable of tracking the player's credit balance,wherein initiating play of a round of a game adds a wager amount to theplayer's credit balance and the game logic may assign at least onelosing outcome to the player's credit balance after the completion of around such that long term statistical house retention on wagers on thegame apparatus is greater than 0% of all wagers.
 5. A method of playinga wagering game comprising: a player initiating play of the wageringgame by placing value at risk; at least the player receiving randomlyprovided sets of symbols for use in the game; evaluating a player'sreceived randomly provided set of symbols according to at least one ofpredetermined rules of count, order, sets, matching symbols, rank ofsymbols, rank of combination of symbols, alignment of symbols, andnumbers of triggering symbols; assigning, tying outcomes with net tyingeffects, winning outcomes with net winning effects and losing outcomeswith net losing effects based on received randomly provided sets ofsymbols; wherein frequency of net winning outcomes for the player exceedfrequency of net losing outcomes for the player and magnitude of winningeffects and magnitude of losing effects under the rules for the gamestatistically assure house retention on wagers that is greater than 0%of all wagers.
 6. The method of claim 5 wherein symbols are randomlyprovided by playing cards.
 7. The method of claim 5 wherein symbols arerandomly provided by spinning of a physical reel on a slot machine. 8.The method of claim 5 wherein symbols are randomly provided by a randomnumber generator providing symbols on a display screen.
 9. The method ofclaim 8 wherein a player places value at risk by placing a wager of aplayer-selected amount on a round of play of the wagering game.
 10. Themethod of claim 8 wherein a player places value at risk by a processorallotting a player-selected amount of credit to the player's creditwhile placing at risk an amount of credit greater than theplayer-selected wager amount.
 11. The method of claim 8 whereinsummation of probabilities of net winning events multiplied by winningpayback odds for each net winning event is less than summation ofprobabilities of net losing events multiplied by losing deduction oddsfor each net losing event.
 12. The method of claim 8 wherein frequencyof net winning events plus frequency of net tying events exceeds 60% ofall wagering outcomes.
 13. The method of claim 8 wherein frequency ofnet winning events exceeds 60% of all wagering outcomes.
 14. The methodof claim 8 wherein at least one net losing event has a magnitude of losseffect that exceeds at least the magnitude of 90% of all winning events.15. A computerized wagering game apparatus for wagering by a player,comprising: a game controller having a processor, memory, a randomnumber generator and game logic capable of generating at least one netwinning or net losing outcome with assigned probabilities, wherein allpossible net outcomes for the player comprise a probability distributionwith an overall mean μ and an overall standard deviation σ, whereinthere exists a subset S of relatively small magnitude net outcomesconsisting of those net outcomes that are greater than μ−√2σ and areless than μ+√2σ, wherein there exists a subset L of relatively largemagnitude net outcomes consisting of those net outcomes that are lessthan or equal to μ−√2σ or are greater than or equal to μ+√2σ, whereinthe mean of net outcomes calculated over subset S is greater than zeroor the mean of net outcomes calculated over subset L is less than zero.